1. Field of the Invention
The present invention relates to a method and a circuit for detecting movements through micro-electric-mechanical sensors, compensating parasitic capacitances and spurious movements.
2. Description of the Related Art
As is known, the use of micro-electric-mechanical sensors, or MEMS sensors, with differential capacitive unbalance has been proposed for forming, for example, linear or rotational accelerometers and pressure sensors.
In particular, MEMS sensors of the indicated type comprise a fixed body (stator) and a moving mass, generally made of suitably doped semiconductor material, connected to each other through elastic elements (springs) and restrained so that, with respect to the stator, the moving mass has predetermined translational and rotational degrees of freedom. Moreover, the stator and the moving mass have a plurality of fixed and, respectively, moving arms, interleaved to each other. In practice, each fixed arm is arranged between a pair of moving arms, so as to form a pair of capacitors having a common terminal and a capacitance which is a function of the relative position of the arms, that is on the relative position of the moving mass with respect to the stator. When the sensor is stressed, the moving mass moves and the capacitance of the capacitors is unbalanced.
Depending on the type of structure and relative movement allowed between the moving mass and the stator, it is possible to manufacture MEMS sensors of a linear or rotational type, with variable interspace (distance between each moving arm and the respective fixed arms) and/or with variable facing area (variation of the reciprocal facing area between the moving arms and the respective fixed arms).
In all mentioned cases, reading by the sensor (that is the detection of an electric quantity representing the variation of the capacitance of the capacitors) leads to problems due to the presence of parasitic capacitances (pad and substrate capacitances).
To overcome this problem, a method and a circuit for reading MEMS sensors have been proposed in “A Three-Axis Micromachined Accelerometer with a CMOS Position-Sense Interface and Digital Offset-Trim Electronics” by M. Lemkin, B. Boser, IEEE Journal of Solid-State Circuits, Vol. 34, N. 4, Pages 456-468.
In the mentioned article, in particular, reference is made to a sensor MEMS 1 of linear type, illustrated, for greater clarity, in FIGS. 1 and 2; however, the following description applies to MEMS sensors of any type.
In detail, the sensor 1 comprises a stator 2 and a moving mass 3, connected to each other by springs 4 so that the moving mass 3 can translate parallel to a first reference axis X, while it is substantially fixed with respect to a second and a third reference axis Y, Z. The sensor 1 is also symmetrical with respect to a longitudinal axis parallel to the first reference axis X.
The a stator 2 and the moving mass 3 are provided with a plurality of first and second fixed arms 5′, 5″ and, respectively, with a plurality of moving arms 6, extending substantially parallel to the plane Y-Z.
As shown in detail in FIG. 2, each moving arm 6 is arranged between two respective fixed arms 5′, 5″, partially facing them. Consequently, the moving arm 6 forms with the two fixed arms 5′, 5″ a first and, respectively, a second detection capacitor 8, 9 with parallel flat faces. In particular, the area of the plates of the detection capacitors 8, 9 is equal to the facing area A of the moving arms 6 and of the fixed arms 5′, 5″. In particular, the facing area A is substantially a rectangle with sides Ly, Lz.
The first and the second detection capacitor 8, 9 have a first and, respectively, a second detection capacitance Ca, Cb, given by the equations:                     Ca        =                  ɛ          ⁢                      A            X1                                              (        1        )                                Cb        =                  ɛ          ⁢                      A            X2                                              (        2        )            where X1, X2 are the distances between the moving arm 6 and the first and, respectively, the second fixed arms 5′, 5″ of FIG. 2 and ∈ is the dielectric constant of the air.
In the sensor 1, all the detection capacitances Ca formed between the moving arms 6 and the first fixed arms 5′ are parallel-connected; similarly all the detection capacitances Cb formed between the moving arms 6 and the second fixed arms 5″ are parallel-connected. Consequently, altogether two capacitances are present between the stator 3 and the moving mass 4, equal to C1=N*Ca and, respectively, to C2=N*Cb, with N number of moving arms 6 of the sensor 1. If we define as the common detection capacitance Cs of the sensor 1 the value of the capacitances C1, C2 at rest, we have:Cs=C1=C2  (3)
After a movement of the moving arm 4 purely along the axis X, the detection capacitances C1, C2 present variations with an opposite sign and with a same absolute value, and equal to a capacitive unbalance ΔCs.
FIG. 3, showing a simplified electric equivalent of the sensor MEMS 1, shows a detection circuit 10, of the type described in the article mentioned.
In particular, the sensor MEMS 1 is schematized by a first and a second equivalent detection capacitor 11, 12, having first terminals connected to a first and, respectively, a second detection node 13, 14 and second terminals connected to a common node 15. Moreover, the first and the second equivalent detection capacitor 11, 12 have capacitances equal to the first and, respectively, to the second detection capacitance C1, C2. The first and the second detection node 13, 14 are connected to all the first arms 5′ and, respectively, to all the second arms 5″ of the stator 3, while the common node 15 is connected to the moving mass 4 and therefore to the moving arms 6. Moreover, in FIG. 3 the parasitic capacitances of the sensor MEMS 1 are schematized by parasitic capacitors 17, 18 connected between the detection nodes 13, respectively 14, and the mass.
The detection circuit 10 comprises a detection operational amplifier 20 in a charge integration configuration and a feedback stage 21.
In detail, the detection operational amplifier 20, having a completely differential topology, has an inverting input connected to the first detection node 13 and a non-inverting input connected to the second detection node 14; and it has a non-inverting output 20a and an inverting output 20b between which is an output voltage Vo. Moreover, a first and a second integration capacitor 22, 23, having a same integration capacitance Ci, are connected one between the inverting input and the non-inverting output 20a and the other between the non-inverting input and the inverting output 20b of the detection operational amplifier 20.
The feedback stage 21 comprises an amplifying circuit 25 and a first and a second feedback capacitor 26, 27, having first terminals connected to an output 25a of the amplifying circuit 25 and second terminals connected to the first and, respectively, to the second detection node 13, 14. The amplifying circuit 25, the structure and operation whereof are described in detail in the mentioned article, is a switched-capacitors circuit having a first and a second differential input 25b, 25c, connected to the inverting input and, respectively, to the non-inverting input of the detection operational amplifier 20, and a reference input, connected to a voltage generator 29 that supplies a first reference voltage Vr1. In practice, the amplifying circuit 25, in a first operative step, detects the voltage between the differential inputs 25b, 25c, determines their mean value and, in a second step, outputs a feedback voltage VFB proportional to the difference between this mean value and the first reference voltage Vr1.
The reading by the sensor MEMS 1 is performed supplying the moving mass 4 with a detection voltage Vs with square wave. The feedback stage 20 intervenes so as to maintain the first and the second detection node 13, 14 at a constant voltage. In particular, the feedback voltage VFB supplied by the amplifying circuit 25 is a square wave in phase-opposition with respect to the detection voltage Vs. In this way, the parasitic capacitors 17, 18 have no influence, since they are maintained at a constant voltage and do not absorb any charge, thereby eliminating the error due to the parasitic capacitances of the sensor MEMS 1. The output voltage Vo between the outputs 20a, 20b of the detection operational amplifier 20 is given by the equation:                     Vo        =                  2          ⁢          Vs          ⁢                                    Δ              ⁢                                                           ⁢              Cs                        Ci                                              (        4        )            wherein, as mentioned previously, ΔCs is the capacitive unbalance of the sensor MEMS 1, that is the capacitance variation of the first and of the second equivalent detection capacitor 11, 12 after movements of the moving mass 4.
The precision of the detection circuit described, however, is limited by another problem, caused by spurious movement, that are not consistent with the allowed degree of freedom and due to the non-ideal nature of the mechanical restraints.
In greater detail, supposing for simplicity's sake that the distances X1, X2 are initially the same and equal to a rest distance X0, from equations (1)-(3) it results that the component ΔCsx of the capacitive unbalance ΔCs according to the first reference axis X is given by the equation:                               Δ          ⁢                                           ⁢          CSx                =                                            -                                                ⅆ                  Cs                                                  ⅆ                  X                                                      ⁢            Δ            ⁢                                                   ⁢            X                    =                                                                      ɛ                  ⁢                                                                           ⁢                  A                                                  X0                  2                                            ⁢              Δ              ⁢                                                           ⁢              X                        =                                          Cs                X0                            ⁢              Δ              ⁢                                                           ⁢              X                                                          (        5        )            where ΔX is the movement of the moving mass 4 along the first reference axis X.
In presence of a spurious movement ΔY parallel to the second reference axis Y, the capacitive unbalance ΔCs has a component ΔCsy given by the equation:                               Δ          ⁢                                           ⁢          CSy                =                                            -                                                ⅆ                  Cs                                                  ⅆ                  Y                                                      ⁢            Δ            ⁢                                                   ⁢            Y                    =                                                    -                                                      ɛ                    ⁢                                                                                   ⁢                    Ly                                    X0                                            ⁢              Δ              ⁢                                                           ⁢              Y                        =                                          -                                  CS                  Ly                                            ⁢              Δ              ⁢                                                           ⁢              Y                                                          (        6        )            
Any spurious movements ΔZ along the third reference axis Z are instead compensated by virtue of the axial symmetry of the sensor MEMS 1.
While the unbalance introduced by the movement ΔX is of a differential type and is itself suitable to be detected by the detection operational amplifier 20, which has a completely differential topology, the movement ΔY introduces a notable common mode variation of the common detection capacitance Cs, as it causes a variation of the facing area A (FIG. 2).
Since the output voltage Vo is directly proportional to the capacitive unbalance ΔCs, which in turn is directly proportional to the common detection capacitance Cs, the common mode variation due to the movement ΔY introduces a significant detection error.